Lecture #34 OUTLINE The MOS Capacitor: • MOS non-idealities (cont.) • VT adjustment Reading: Chapter 18.3 Spring 2007 EE130 Lecture 34, Slide 1 Poly-Si Gate Depletion • A heavily doped film of polycrystalline silicon (poly-Si) is typically employed as the gate-electrode material in modern MOS devices. NMOS PMOS N+ poly-Si P+ poly-Si P-type Si n-type Si – There are practical limits to the electrically active dopant concentration (usually less than 1x1020 cm-3) The gate must be considered as a semiconductor, rather than a metal Spring 2007 EE130 Lecture 34, Slide 2 MOS Band Diagram with Gate Depletion Si biased to inversion: WT Ec qVpoly qfS EFS Ev Qinv Cox (VG V poly VT ) qVG Ec Ev VG is effectively reduced: W poly 2 SiV poly qN poly Wpoly N+ poly-Si gate Spring 2007 P-type Si EE130 Lecture 34, Slide 3 How can gate depletion be minimized? Gate Depletion Effect Gauss’s Law dictates Wpoly oxEox / qN poly xo is effectively increased: 1 N+ poly-Si Cpoly + + + + + + + + Cox N+ - - - - - - - - - p-type Si xo 1 W poly 1 C C SiO C ox poly Si 2 SiO 2 xo (W poly / 3) Qinv (VG VT ) Spring 2007 EE130 Lecture 34, Slide 4 SiO 2 xo (W poly / 3) 1 Example: GDE Vox , the voltage across a 2 nm thin oxide, is 1 V. The n+ poly-Si gate active dopant concentration Npoly is 8 1019 cm-3 and the Si substrate doping concentration NA is 1017cm-3. Find (a) Wpoly , (b) Vpoly , and (c) VT . Solution: (a) Wpoly oxEox / qN poly oxVox / x o qN poly 3.9 8.85 10 14 (F/cm) 1 V 7 19 3 19 2 10 cm 1.6 10 C 8 10 cm 1.3 nm Spring 2007 EE130 Lecture 34, Slide 5 (b) W poly 2 SiV poly qN poly 2 Vpoly qN polyWpoly / 2 Si 0.11 V (c) VT VFB 2fF Vox V poly EG kT N A 0.98 V VFB ln 2q q ni VT 0.98 V 0.84 V 1 V 0.11 V 0.97 V Is the loss of 0.11V significant? Spring 2007 EE130 Lecture 34, Slide 6 Inversion-Layer Thickness Tinv The average inversion-layer location below the Si/SiO2 interface is called the inversion-layer thickness, Tinv . poly-Si gate SiO2 Si Electron Density Quantum mechanical theory -50 -40 -30 -20 -10 Spring 2007 0 10 20 EE130 Lecture 34, Slide 7 30 40 50 Å Effective Oxide Thickness, Toxe Toxe W poly Tinv xo 3 3 at VG=Vdd (VG + VT)/Toxe can be shown to be the average electric field in the inversion layer. Tinv of holes is larger than that of electrons because of the difference in effective masses. Spring 2007 EE130 Lecture 34, Slide 8 Effective Oxide Capacitance, Coxe Tox xo W poly / 3 Tinv / 3 Qinv ox Toxe (VG VT ) Coxe (VG VT ) C Cox Basic LF C-V with gate-depletion with gate-depletion and charge-layer thickness data VG Spring 2007 EE130 Lecture 34, Slide 9 VT Adjustment by Ion Implantation • In modern IC fabrication processes, the threshold voltages of MOS transistors are adjusted by ion implantation: – A relatively small dose NI (units: ions/cm2) of dopant atoms is implanted into the near-surface region of the semiconductor – When the MOS device is biased in depletion or inversion, the implanted dopants add to the dopant-ion charge near the oxide-semiconductor interface. qN I VT Cox Spring 2007 N I 0 for donor atoms N I 0 for acceptor atoms EE130 Lecture 34, Slide 10